And yet, parameterized inspiral tests are not all exactly the same;
they can differ in the underlying GR waveform model, in how the
non-GR parameters are introduced into it, and in the transition
beyond the inspiral part. In this work, we develop a framework to
examine how the details of the construction of parameterized waveform
models systematically affect the tests of GR in which they are
employed Parts of this manuscript are based on the PhD
thesis of Noah Sennett [1]}, in particular Sec. 
follows Chapter 9 of Ref. [1]}.. It is also important
to be able to distinguish deviations from GR due to systematic uncertainties
of the waveform model from true violations of the theory. This infrastructure
allows us to add generic corrections to the inspiral portion of any
gravitational waveform, thereby allowing tests of GR
with a broader range of waveform models than previously
possible (e.g., with the TIGER infrastructure [3]}, [4]}).
We call this framework the flexible theory-independent (FTI) approach, and
explore it using synthetic binary BH (BBH) GW signals. In addition,
the conveniently adaptable design of the FTI framework allows us for
easy construction of waveform models for theory-specific tests. As an
example, we apply the FTI framework to the first binary NS
(BNS) merger observed by the LIGO and Virgo detectors, GW170817, and
set bounds on the Jordan-Fierz-Brans-Dicke (JFBD) scalar-tensor theory
of gravity. We note that the FTI approach has already been
extensively used by LIGO and Virgo data analysts in
Refs. [5]}, [6]}, [7]}, [8]} and
also by some of the authors of this manuscript in Ref. [9]}.
